Alicia Dickenstein: Non-Koszul syzygies of bihomogeneous polynomials

Abstract: Fix  a positive bidegree d  and let I be an ideal generated by three bihomogeneous polynomials of bidegree d without common zeros in \(P^1 \times P^1\). In joint work with Nicolas Botbol and Hal Schenck, we study the possible minimal free resolutions of I.  We show that there are many possible resolutions.

In case the given polynomials are generic, we have a conjecture for the dimension of the non-Koszul syzygies in any bidegree that explains all computations. On the other side, Ralf Fr\"oberg has a conjecture for the dimension of the quotient by I in any bidegree. I will discuss the equivalence of these two conjectures.